Well since the problem doesn't come from !
But indeed, that's not a model of the whole formula: there is no element strictly greater than in that set. (if is a strict order, that's what says : for any there is a such that )

So using a set whose elements are integers, a model would be...

Last edited by clic-clac; February 23rd 2009 at 01:39 PM.
Reason: orth

Since a strict order satisfies the two last parts of your formula, if we find a set and a strict order on that set which satisfy the first part of the formula, we have a model.

So assume is a strict order, the first part: means that if you take any element in your set, then you can find another element which is strictly greater. A consequence is that your set can't have a greatest element. So for instance, a simple model is

Of course, there are a lot of other models. Another one quite simple is the set of all primes with the same order.

Last edited by clic-clac; February 23rd 2009 at 02:02 PM.
Reason: orth